Inequalities in Exposure to Firearm Violence by Race, Sex, and Birth Cohort From Childhood to Age 40 Years, 1995-2021

Key Points Question Did the likelihood of being shot, seeing someone shot, or living near firearm violence vary by race, sex, and birth cohort over the life course during the past 3 decades? Findings This cohort study found that the likelihood of exposure to all forms of firearm violence varied significantly and persistently over the life course by race. Sex differences were greatest for being shot compared to witnessing or proximity to firearm violence, and cohort differences were most pronounced for witnessing violence. Meaning These finding suggest that understanding who gets exposed to firearm violence and when requires simultaneous attention to inequality by race, sex, and cohort.

This supplemental material has been provided by the authors to give readers additional information about their work.

eAppendix 1. Survey Measures
The following survey questions were used to create age-specific measures of exposure to firearm violence and personal firearm victimization.
Age when first witnessed someone being shot ("seen shot") was calculated from several questions across the study period.

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Wave 1 (1981, 1984, and 1987 cohorts) -"Have you ever seen or been present when someone was shot?" -"When was the last time you saw that?" • Wave 2 (1981, 1984, and 1987 cohorts) -"In your whole life, have you ever seen someone else get shot?" -"Now just thinking about the last 12 months, have you seen someone get shot?" -"How old were you the first time you saw this?" • Wave 3 (1981, 1984, and 1987 cohorts) -"In your whole life, have you ever seen someone else get shot?" -"Now just thinking about the last 12 months, have you seen someone get shot?" • Wave 5 (1981, 1984, 1987, and 1996 cohorts) -"In your whole life, have you ever seen someone else get shot?" -"Now just thinking about the past 12 months, have you ever seen someone else get shot?" Age at first personal gunshot victimization ("been shot") was calculated in a similar manner, relying on questions at Waves 2, 3 and 5.
• Wave 2 (1981, 1984, and 1987 cohorts) -"In your whole life, have you ever been shot?" -"Now just thinking about the last 12 months, have you been shot?" • Wave 3 (1981, 1984, and 1987 cohorts) -"In your whole life, have you ever been shot?" -"About how old were you the first time this happened?" -"Now just thinking about the last 12 months, have you been shot?" • Wave 5 (1981,1984,1987, and 1996 cohorts) -"In your whole life, have you ever been shot?" -"How old were you when this first happened?" No survey questions regarding exposure to firearm violence and victimization were asked in the wave 4 survey.

eAppendix 2. Accelerated Failure Time Models
The SPT models in the main text and Cox models above make a proportional hazards assumption-covariates influence survival by proportionally increasing or decreasing a common age-specific baseline hazard. When the proportional hazards assumption is violated, estimated hazard ratios will be biased. Additionally, SPT and Cox models estimate the baseline hazard non-parametrically, permitting it to conform closely to the data and avoiding bias that may result from mis-specified parametric baseline hazards. In contrast, accelerated failure time (AFT) models assume covariates influence survival by multiplicatively accelerating or decelerating a parametrically-specified survival function. That is, rather than assuming covariates scale a non-parametric baseline hazard upward and downward, covariates multiplicatively increase or decrease the rate of progression through a common parametric baseline survival curve. Due to the sensitivity of AFT models to the choice of parametric specification, proportional hazard models are typically considered the default approach for modeling time-to-event data, so long as the proportional hazards assumption appears warranted. In the present case, interval censoring prevents formal tests of the proportional hazards assumption, but non-parametric (i.e., NPMLE) survival curves (figure 2) and theoretical expectations provide guidance.
Theoretically, we expect the proportional hazards assumption to be more tenable for race and sex covariates: these will increase or decrease the hazard of exposure, which generally follows a shared non-monotonic, unimodal hazard curve that emerges as a result of the age crime curve and changes in routine activities over the life course. That is, it seems reasonable to expect members of some demographic groups to have a fixed multiplicatively higher likelihood of seeing shootings or being shot at any given age. Evidence in support of this is provided by the survival curves in figure 2, panels A-D which generally appear to shift proportionally across sex and race.
We expect the proportional hazards assumption to be less tenable for the cohort differences. For the oldest three cohorts, firearm homicide in Chicago was at its highest from 1990 to 1995 and then precipitously declined for ten years. As a result, the 1981 cohort experienced a context of high-violence well into adolescence while violence had declined greatly by the time the 1987 cohort entered adolescence. The 1996 cohort, in contrast, lived in a low violence context until the end of adolescence. As a result, each cohort's period of peak violence occurred at a different age. We would expect this results in both a proportional hazards shift-due to differences in overall level of violence-and an acceleration of failure time-as risk of exposure is highest during peak periods. In support of the latter expectation, the survival curves in figure 2, panels E and F, share a similar shape shifted forward and backward between cohorts. The highest expected exposure should have occurred when peak environmental risk overlapped with high age-specific risk (i.e., for the 1981 cohort), though the models cannot account for both simultaneously while addressing interval censoring.
AFT models may be more appropriate for modeling cohort differences as they relax the proportional hazards assumption and instead model acceleration of failure time. However, AFT estimates may be biased if the baseline hazard curve is misspecified. eFigure 2 depicts results from five common AFT baseline parameterizations. Estimates were similar across all specifications and to the proportional hazards models-except for cohorts, where differences are larger in AFT models. The log-normal specification produces the best AIC value in all cases except for been shot with survey weights where the log-logistic parameterization is slightly preferred (though similar to Weibull, gamma, and generalized gamma). Models using the highly flexible three parameter generalized gamma distribution-which makes strong demands of the data-failed to converge for the seen shot outcome. In all cases the results from AFT models closely parallel those from the main-text SPT models in direction, relative magnitude, and statistical significance (see figure 2), both with and without survey weights (see eFigure 3, panels A and B).